TY - JOUR
T1 - W2,p -estimates for surfaces in terms of their two
fundamental forms
AU - Ciarlet, Philippe G.
AU - Mardare, Cristinel
PY - 2018/1
Y1 - 2018/1
N2 - Let p>2. We show how the fundamental theorem of surface theory for surfaces of class W2,ploc(ω) over a simply-connected open subset of R2 established in 2005 by S. Mardare can be extended to surfaces of class W2,p(ω) when ω is in addition bounded and has a Lipschitz-continuous boundary. Then we establish a nonlinear Korn inequality for surfaces of class W2,p(ω). Finally, we show that the mapping that defines in this fashion a surface of class W2,p(ω), unique up to proper isometries of E3, in terms of its two fundamental forms is locally Lipschitz-continuous.
AB - Let p>2. We show how the fundamental theorem of surface theory for surfaces of class W2,ploc(ω) over a simply-connected open subset of R2 established in 2005 by S. Mardare can be extended to surfaces of class W2,p(ω) when ω is in addition bounded and has a Lipschitz-continuous boundary. Then we establish a nonlinear Korn inequality for surfaces of class W2,p(ω). Finally, we show that the mapping that defines in this fashion a surface of class W2,p(ω), unique up to proper isometries of E3, in terms of its two fundamental forms is locally Lipschitz-continuous.
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85038858056&origin=recordpage
U2 - 10.1016/j.crma.2017.12.003
DO - 10.1016/j.crma.2017.12.003
M3 - RGC 21 - Publication in refereed journal
VL - 356
SP - 85
EP - 91
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 1
ER -